The Golomb topology of polynomial rings, II

AbstractAbstractWe study the interplay of the Golomb topology and the algebraic structure in polynomial rings K [X] over a field K. In particular, we focus on infinite fields K of positive characteristic such that the set of irreducible polynomials of K [X] is dense in the Golomb space G(K [X]). We show that, in this case, the characteristic of K is a topological invariant, and that any self-homeomorphism of G(K [X]) is the composition of multiplication by a unit and a ring automorphism of K [X].Mathematics Subject Classification (2020): 54G9913F2013F0512E99Key words: Golomb topologypolynomial ringsDedekind domains